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VRSQRT28SS—Approximation to the Reciprocal Square Root of Scalar Single-Precision Floating-Point Value with Less Than 2^-28 Relative Error

Opcode/Instruction Op /En 64/32 bit Mode Support CPUID Feature Flag Description

EVEX.NDS.LIG.66.0F38.W0 CD /r

VRSQRT28SS xmm1 {k1}{z}, xmm2, xmm3/m32 {sae}

T1S V/V AVX512ER Computes approximate reciprocal square root (<2^-28 relative error) of the scalar single-precision floating-point value from xmm3/m32 and stores result in xmm1with writemask k1. Also, upper 3 single-precision floating-point value (bits[127:32]) from xmm2 is copied to xmm1[127:32].

Instruction Operand Encoding

Op/En Operand 1 Operand 2 Operand 3 Operand 4
T1S ModRM:reg (w) EVEX.vvvv (r) ModRM:r/m (r) NA


Computes the reciprocal square root of the low float32 value in the second source operand (the third operand) and store the result to the destination operand (the first operand). The approximate reciprocal square root is evaluated with less than 2^-28 of maximum relative error prior to final rounding. The final result is rounded to < 2^-23 rela-tive error before written to the low float32 element of the destination according to the writemask k1. Bits 127:32 of the destination is copied from the corresponding bits of the first source operand (the second operand).

If any source element is NaN, the quietized NaN source value is returned for that element. Negative (non-zero) source numbers, as well as -∞, return the canonical NaN and set the Invalid Flag (#I).

A value of -0 must return -∞ and set the DivByZero flags (#Z). Negative numbers should return NaN and set the Invalid flag (#I). Note however that the instruction flush input denormals to zero of the same sign, so negative denormals return -∞ and set the DivByZero flag.

The first source operand is an XMM register. The second source operand is an XMM register or a 32-bit memory location. The destination operand is a XMM register.

A numerically exact implementation of VRSQRT28xx can be found at


VRSQRT28SS (EVEX encoded versions)
IF k1[0] OR *no writemask* THEN
    DEST[31: 0] (cid:197) (1.0/ SQRT(SRC[31: 0]));
    IF *merging-masking*
        ; merging-masking
        THEN *DEST[31: 0] remains unchanged*
        ; zeroing-masking
        DEST[31: 0] (cid:197) 0
DEST[127:32] (cid:197) SRC1[127: 32]
DEST[MAX_VL-1:128] (cid:197) 0

Table 5-30. VRSQRT28SS Special Cases

Input value Result value Comments
NAN QNAN(input) If (SRC = SNaN) then #I
X = 2-2n 2n
X < 0 QNaN_Indefinite Including -INF
X = -0 or negative denormal -INF #Z
X = +0 or positive denormal +INF #Z
X = +INF +0

Intel C/C++ Compiler Intrinsic Equivalent

VRSQRT28SS __m128 _mm_rsqrt28_round_ss(__m128 a, __m128 b, int sae);
VRSQRT28SS __m128 _mm512_mask_rsqrt28_round_ss(__m128 s, __mmask8 m,__m128 a,__m128 b, int sae);
VRSQRT28SS __m128 _mm512_maskz_rsqrt28_round_ss(__mmask8 m,__m128 a,__m128 b, int sae);

SIMD Floating-Point Exceptions

Invalid (if SNaN input), Divide-by-zero

Other Exceptions

See Exceptions Type E3.